Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Abstract

Potentials are constructed for the lambda-nucleon interaction in the ${}^1{\text{S}}_0$ and ${}^3{\text{S}}_1$ channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel'fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambda-nucleon force in the ${}^1{\text{S}}_0$ channel is observed to be stronger than in the ${}^3{\text{S}}_1$ channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.

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Cited by in corpus (1)

• Faddeev calculations on lambda hypertriton with potentials from Gel'fand-Levitan-Marchenko theory